What is the value of cos(80)cos(20)+sin(80)sin(20) ?

The value of cos(80)cos(20)+sin(80)sin(20) is 1/2

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cos(80)cos(20)+sin(80)sin(20)

cos (8 0^{\circ}) cos (2 0^{\circ}) + sin (8 0^{\circ}) sin (2 0^{\circ})

\frac{1}{2}

Solution steps

cos (8 0^{\circ}) cos (2 0^{\circ}) + sin (8 0^{\circ}) sin (2 0^{\circ})

Rewrite using trig identities:

cos (6 0^{\circ})

= cos (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

= \frac{1}{2}

sec (arctan (\frac{7}{8}))

cos^{4} (\frac{π}{2})

cos (11 2^{\circ})

- sin (\frac{5 π}{2})

arccos (\frac{13}{41 \cdot 34})

What is the value of cos(80)cos(20)+sin(80)sin(20) ?
The value of cos(80)cos(20)+sin(80)sin(20) is 1/2